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Explore the mathematical concepts of theta lifts and holomorphic projection in this conference talk delivered by Micheal Griffin at the International Centre for Theoretical Sciences. Delve into advanced topics within the framework of harmonic Maass forms and mock modular forms, examining how theta lifts serve as powerful tools for constructing modular forms and their generalizations. Learn about the intricate relationship between theta functions and holomorphic projection techniques, understanding their applications in number theory and representation theory. Discover how these mathematical constructs connect to Ramanujan's mysterious mock theta functions and their modern interpretations through the lens of harmonic Maass forms. Gain insights into the theoretical foundations that underpin recent developments in modular form theory, including connections to partition theory, elliptic curves, and black hole physics. Examine the sophisticated mathematical machinery that has emerged from Zwegers', Bruinier's, and Funke's groundbreaking work in establishing the proper framework for understanding mock modular forms and their holomorphic components.
